It's either in anti-theft mode, which I don't think existed yet in '88, or you're losing fuel pressure. Monitor the voltage to the positive wire on the ignition coil to see if the 12 volts goes away when the engine stalls. If it stays there UNTIL the engine stops rotating, you have a fuel pump circuit problem. If the voltage to the coil goes to 0 volts and THEN the engine stops, you don't have a fuel or ignition problem. You have a problem with what both of those circuits have in common, and that's the Hall Effect pickup in the distributor.